I believe this went live yesterday with patch 4.0.0, so everyone can download the game. Not sure if the campaigns are completely free or just slightly more multiplayer stuff than was previously available.

Here is a specific rundown of everything that will be available to you for free:

The original Wings of Liberty campaign. Experience the original epic campaign that kicked off the StarCraft II saga! If you picked up Wings of Liberty previously but haven’t come back to StarCraft II in a while, we’ve got good news for you too—if you purchased Wings of Liberty prior to October 31, 2017, you’ll receive the second installment in StarCraft II’s campaign, the zerg-focused Heart of the Swarm, as a limited time offer from November 8 to December 8. Make sure to log in during that window to claim it!

You will be able to access the ranked multiplayer ladder to compete with other players to become the best of the best, complete with all of the multiplayer units from Wings of Liberty, Heart of the Swarm, and Legacy of the Void. All you have to do to unlock it permanently is earn 10 First Wins of the Day in Unranked or Versus A.I. play—our way to preserve the quality and integrity of the ranked experience.

Current and upcoming Co-op Commanders are available to play for free up to level five, and the level restriction for weekly mutations has been removed. You’ll be able to tackle these extra challenging missions with your friends right away. The Co-op Commanders Raynor, Kerrigan, and Artanis will remain completely free, meaning that you can keep leveling them to your heart’s content.

Campaign mission design has gotten quite a bit more sophisticated since the 90s; plenty of missions are of the hero RPG variety with no basebuilding or offer objectives other than the standard annihilation type.